On the Second-Order Shape Derivative of the Kohn-Vogelius Objective Functional Using the Velocity Method
The exterior Bernoulli free boundary problem was studied via shape optimization technique. The problem was reformulated into the minimization of the so-called Kohn-Vogelius objective functional, where two state variables involved satisfy two boundary value problems, separately. The paper focused on...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2015/954836 |
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| Summary: | The exterior Bernoulli free boundary problem was studied via shape optimization technique. The problem was reformulated into the minimization of the so-called Kohn-Vogelius objective functional, where two state variables involved satisfy two boundary value problems, separately. The paper focused on solving the second-order shape derivative of the objective functional using the velocity method with nonautonomous velocity fields. This work confirms the classical results of Delfour and Zolésio in relating shape derivatives of functionals using velocity method and perturbation of identity technique. |
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| ISSN: | 1687-9643 1687-9651 |